Abstract: System identification from free response time decay history data of a dynamic system employs a new closed form shape fit for solving the dynamic system free response decay equation. The closed form shape fit allows for the treatment of the mode shapes as linear coefficients and allows the mode shapes for each sensor to be computed independently, thereby reducing computation time. The closed form shape fit efficiently provides mode shapes for a large set of sensors based on a fit from a small set of sensors. The closed form shape fit combined with a non-linear fit of frequency and damping characteristics efficiently estimates the optimal solution, thereby reducing the time to completion of non-linear optimization. A nonlinear optimization can incorporate the closed form shape fit into determining the Jacobian matrix of sensitivities and evaluating the residuals, thereby reducing the number of parameters and reducing the time to completion of the non-linear optimization.

Abstract: System identification from free response time decay history data of a dynamic system employs a new closed form shape fit for solving the dynamic system free response decay equation. The closed form shape fit allows for the treatment of the mode shapes as linear coefficients and allows the mode shapes for each sensor to be computed independently, thereby reducing computation time. The closed form shape fit efficiently provides mode shapes for a large set of sensors based on a fit from a small set of sensors. The closed form shape fit combined with a non-linear fit of frequency and damping characteristics efficiently estimates the optimal solution, thereby reducing the time to completion of non-linear optimization. A nonlinear optimization can incorporate the closed form shape fit into determining the Jacobian matrix of sensitivities and evaluating the residuals, thereby reducing the number of parameters and reducing the time to completion of the non-linear optimization.

Abstract: Methods and systems for analyzing flutter test data using non-linear transfer function frequency response fitting are provided. In one embodiment, a plurality of data points are read, with each data point representing a motion of an aeroelastic structure (e.g. an aircraft surface) at a different location. A closed form fit to the plurality of data points is performed to obtain an initial curve fit condition. At least one non-linear transfer function frequency response curve fit is then performed to the plurality of data points.

Abstract: Methods and apparatus for analyzing flutter test data using damped sine curve fitting. In one embodiment, a plurality of data points are read, with each data point representing an amplitude versus a test time. A number “N” of damped sine waves to fit to the plurality of data points is determined, and the number “N” of damped sine waves is fit to the plurality of data points using a non-linear “N” damped sine wave fitting algorithm.

Abstract: Methods and systems for analyzing flutter test data using non-linear transfer function frequency response fitting are provided. In one embodiment, a plurality of data points are read, with each data point representing a motion of an aeroelastic structure (e.g. an aircraft surface) at a different location. A closed form fit to the plurality of data points is performed to obtain an initial curve fit condition. At least one non-linear transfer function frequency response curve fit is then performed to the plurality of data points.

Abstract: Methods and apparatus for analyzing of flutter test data using damped sine curve fitting are provided. A plurality of data points are read, with each data point representing an amplitude versus a test time. A number “N” of damped sine waves to fit to the plurality of data points is determined, and the number “N” of damped sine waves is fit to the plurality of data points using a non-linear “N” damped sine wave fitting algorithm.

Abstract: A method and apparatus for directional drilling to recover hydrocarbons, thermal energy, or the like, by using coiled tubing while the well is under pressure so that high density drilling fluids to control the subsurface pressures during drilling are not required. Snubbing apparatus and methods which maintain control of the bore hole pressure throughout the drilling operation are used, thus permitting the use of fresh water as a combination hydraulic fluid to operate a downhole motor and cool the bit, and to flush cuttings from the bore hole. The apparatus uses a down hole assembly including a bit driven by a motor, preferably hydraulic, which is located in a bent housing. A steering tool capable of indicating the angle and azimuth of inclination of the housing is carried by the motor housing and is connected to surface instrumentation by an electrical cable extending through the coiled tubing.

Abstract: A method and apparatus for directional drilling to recover hydrocarbons, thermal energy, or the like, by using coiled tubing while the well is under pressure so that high density drilling fluids to control the subsurface pressures during drilling are not required. Snubbing apparatus and methods which maintain control of the bore hole pressure throughout the drilling operation are used, thus permitting the use of fresh water as a combination hydraulic fluid to operate a downhole motor and cool the bit, and to flush cuttings from the bore hole. The apparatus uses a down hole assembly including a bit driven by a motor, preferably hydraulic, which is located in a bent housing. A steering tool capable of indicating the angle and azimuth of inclination of the housing is carried by the motor housing and is connected to surface instrumentation by an electrical cable extending through the coiled tubing.